Is there a show similar to Rome

No, I do not think so. May be in the near future I hope.

This is something that upsets me quite a bit, as well. Ditto with Ancient Egypt. Both of these eras are extremely neglected when it comes to film and television. And when you do see something that takes place during these time periods, they typically involve supernatural elements (i.e., myths involving Greek gods or nonsense about mummies and curses). It's never anything that strives for realism. Depressingly, the best we can get (that I'm aware of) is something like 300. Or Alexander, maybe.

I suppose much of this is likely due to the lack of information we have about these time periods compared to what all we know about Ancient Rome. However, personally, I believe we know enough to nevertheless make something reasonably realistic. There was a particularly good 3-part documentary series narrated by Liam Neeson called The Greeks: Crucible of Civilization (part of PBS's Empires series) that, itself, contained several real-life narratives that could make for the foundation of a really good drama series, in my opinion.

As someone else mentioned here, the series I, Claudius is a good followup to Rome. It starts chronologically where Rome leaves off, with Augustus's time as emperor, then follows with the story of Tiberius, Caligula, and Claudius (with a little bit of Nero, near the end).

But, really, none of this has a similar feel to Rome. I, Claudius feels more like a stageplay. Crucible of Civilization, while great, is just a documentary. And, as mentioned, The Roman Empire is just your typical Netflix docuseries. Funny enough, the one thing I've watched that felt the most like Rome was Game of Thrones; which I don't believe was very historically accurate lol.

Then there's the Spartacus series, of course, which takes place shortly before Rome. The story to that is more true to life than the comic book look of the show may give the impression. But, tonally, it feels very over the top.